Motivated by the limits of the scalability of numerical SVD computations, there has been a surge of work which has focussed on providing approximate, but more easily computable matrix factorizations. Thanks to advances in our understanding of random matrix theory and high dimensional probability (in particular, concentration of measure), randomized methods have been shown to provide an excellent balance between numerical implementation (in terms of storage requirements and computational cost) and accuracy of approximation (in theory and practice). Broadly speaking this field is referred to as randomized numerical linear algebra (RNLA), and we refer the reader to  [1]}, [2]}, [3]} and the references therein for an overview of the field. In particular, the machine learning and optimization communities have started to adopt RNLA methods into their work flows with great success, see for example [4]}, [5]}.
